On the third break point opportunity for Kohlschreiber, Djokovic inexplicably hit a backhand volley wide to put his opponent 4-2 ahead.
A furious Djokovic went on to smash his racket three times on the court and was met with a chorus of boos from the spectators.
Two-times winner Djokovic would go on to drop his serve for the fourth time in the set but regained his composure with an early break in the decider.
He maintained the advantage to avenge his Indian Wells second-round defeat by Kohlschreiber last month.
"There were lots of ups and downs. It was not the prettiest of matches," Djokovic, who record his 850th tour-level win, said.
"He played well, but a win is a win. This was a tough first match of the clay season.
"I had to figure out how I needed to move, this kind of match can be expected. It was probably good for me to spend so long on the court."
Argentine Guido Pella knocked out seventh seed Marin Cilic, beating the Croatian 6-3 5-7 6-1.
The defeat left 2014 U.S. Open winner Cilic with just one victory from five matches since January's Australian Open, where he was knocked out in the fourth round.
(Reporting by Hardik Vyas in Bengaluru, editing by Pritha Sarkar)
